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# If x and y are positive integers and 1 + x + y + xy = 15,

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Intern
Joined: 06 Nov 2006
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If x and y are positive integers and 1 + x + y + xy = 15, [#permalink]

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01 Dec 2006, 07:26
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If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3
B. 5
C. 6
D. 8
E. 9

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Director
Joined: 06 Feb 2006
Posts: 893

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01 Dec 2006, 07:43
Tennisball's approach is better

Last edited by SimaQ on 01 Dec 2006, 09:04, edited 1 time in total.

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Intern
Joined: 06 Nov 2006
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01 Dec 2006, 07:51
SimaQ wrote:
I choose C...

simplify the given equation to x+y=14-xy

now you see that x+y cannot equal 3, 5 or 9 because in those cases xy would have to be odd number, which is impossible if both numbers are intergers....

So look at C and D....

xy could equal 8 or 6.... however plug in values....

2+3=14-6....cannot hold

4+2=14-8...holds....

Do not know a better way...

I don't understand why x+y can't be 3, 5 or 9.

if x+y=3, so xy=11 (11 * 1)
if x+y=5, so xy=9 (9 * 1 or 3 * 3)
if x+y=9, so xy=5 (5 * 1)

Where am I wrong?

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VP
Joined: 25 Jun 2006
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01 Dec 2006, 07:52
C.

1 + x + y + xy = (x+1)(y+1) = 15.

since x and y are positive integers, x + 1 and y + 1 equal to 3 or 5 .

so x + y = 6.

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01 Dec 2006, 07:52
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